Sparse Recovery with Orthogonal Matching Pursuit under RIP

Details Sparse Recovery with Orthogonal Matching Pursuit under RIP Sparse Recovery with Orthogonal Matching Pursuit under RIP

2010-05-13

arxiv.org/abs/1005.2249v2

Computer Science

Information Theory

Scientific paper

This paper presents a new analysis for the orthogonal matching pursuit (OMP) algorithm. It is shown that if the restricted isometry property (RIP) is satisfied at sparsity level $O(\bar{k})$, then OMP can recover a $\bar{k}$-sparse signal in 2-norm. For compressed sensing applications, this result implies that in order to uniformly recover a $\bar{k}$-sparse signal in $\Real^d$, only $O(\bar{k} \ln d)$ random projections are needed. This analysis improves earlier results on OMP that depend on stronger conditions such as mutual incoherence that can only be satisfied with $\Omega(\bar{k}^2 \ln d)$ random projections.

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